稱形如
f
(
x
)
=
sin
x
{\displaystyle f(x)=\sin x}
(
−
∞
,
+
∞
)
{\displaystyle (-\infty ,+\infty )}
[
−
1
,
1
]
{\displaystyle [-1,1]}
2
π
{\displaystyle 2\pi }
稱形如
f
(
x
)
=
cos
x
{\displaystyle f(x)=\cos x}
(
−
∞
,
+
∞
)
{\displaystyle (-\infty ,+\infty )}
[
−
1
,
1
]
{\displaystyle [-1,1]}
2
π
{\displaystyle 2\pi }
稱形如
f
(
x
)
=
tan
x
{\displaystyle f(x)=\tan x}
{
x
|
x
≠
k
π
+
π
2
,
k
∈
Z
}
{\displaystyle \{x|x\neq k\pi +{\frac {\pi }{2}},\,k\in \mathbb {Z} \}}
(
−
∞
,
+
∞
)
{\displaystyle (-\infty ,+\infty )}
π
{\displaystyle \pi }
稱形如
f
(
x
)
=
cot
x
{\displaystyle f(x)=\cot x}
{
x
|
x
≠
k
π
,
k
∈
Z
}
{\displaystyle \{x|x\neq k\pi ,\,k\in \mathbb {Z} \}}
(
−
∞
,
+
∞
)
{\displaystyle (-\infty ,+\infty )}
π
{\displaystyle \pi }
稱形如
f
(
x
)
=
sec
x
{\displaystyle f(x)=\sec x}
{
x
|
x
≠
k
π
+
π
2
,
k
∈
Z
}
{\displaystyle \{x|x\neq k\pi +{\frac {\pi }{2}},\,k\in \mathbb {Z} \}}
(
−
∞
,
−
1
]
∪
[
1
,
+
∞
)
{\displaystyle (-\infty ,-1]\cup [1,+\infty )}
2
π
{\displaystyle 2\pi }
稱形如
f
(
x
)
=
csc
x
{\displaystyle f(x)=\csc x}
{
x
|
x
≠
k
π
,
k
∈
Z
}
{\displaystyle \{x|x\neq k\pi ,\,k\in \mathbb {Z} \}}
(
−
∞
,
−
1
]
∪
[
1
,
+
∞
)
{\displaystyle (-\infty ,-1]\cup [1,+\infty )}
2
π
{\displaystyle 2\pi }
雙曲正弦 函數：
y
=
sinh
x
=
e
x
−
e
−
x
2
{\displaystyle y=\sinh x={\frac {e^{x}-e^{-x}}{2}}}
雙曲餘弦 函數：
y
=
cosh
x
=
e
x
+
e
−
x
2
{\displaystyle y=\cosh x={\frac {e^{x}+e^{-x}}{2}}}
y
=
tanh
x
=
sinh
x
cosh
x
=
e
x
−
e
−
x
e
x
+
e
−
x
{\displaystyle y=\tanh x={\frac {\sinh x}{\cosh x}}={\frac {e^{x}-e^{-x}}{e^{x}+e^{-x}}}}
反雙曲正弦函數：
y
=
arsinh
x
=
ln
(
x
+
x
2
+
1
)
{\displaystyle y=\operatorname {arsinh} \,x=\ln(x+{\sqrt {x^{2}+1}})}
y
=
arcosh
x
=
ln
(
x
+
x
2
−
1
)
{\displaystyle y=\operatorname {arcosh} \,x=\ln(x+{\sqrt {x^{2}-1}})}
Davenport, J. H.: What Might "Understand a Function" Mean. In: Kauers, M.; Kerber, M., Miner, R.; Windsteiger, W.: Towards Mechanized Mathematical Assistants. Springer, Berlin/Heidelberg 2007, p. 55-65. [1] （頁面存檔備份 ，存於網際網路檔案館 ）
![{\displaystyle [-1,1]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/51e3b7f14a6f70e614728c583409a0b9a8b9de01)
![餘切函數]圖像](/wiki/File:Cotan_proportional.svg)
![{\displaystyle (-\infty ,-1]\cup [1,+\infty )}](https://wikimedia.org/api/rest_v1/media/math/render/svg/5dedf8ddf2dcc93b2f0799dfd206f0064a74e94f)
